Most road transport leaving for Goa, from Mumbai, depart at from 1600 hours onwards, with the last bus leaving at 2200 hours and all arrving in Goa from 700 hours onwards. Suggest that you book the Volvo coaches - AC luxury bus services with recliners that reach a 160-degree angle or so. Very comfortable - insist on the first row, near the entrance, called 'entrance seats' as these have the most legroom and you dont have the fear of the previous seat crushing your knees. I tend to avoid the sleepers, as you can only lie down and not sit up and I find the sleepers uncomfortable. Bus Services are freely available and you can usually find the offices for popular ones all around the city - the names of the bus service providers are- Neeta Volvo, Paulo Travels, Amsons, Kadamba, Modern Volvo, Patel Volvo to name a few.
If you take the train option, then you have a choice of an afternoon train (leaves at about 1400 hours or night train (leaves at 2300 hours.) The AC sleeper coaches are usally booked out, but try and obtain the Indrail pass available for all non-Indians. You get first preference then and priority treatment. The night train is a good idea as you get full days in Mumbai and Goa (it reaches Goa at about 700 hours). If you want to see the countryside, then take the afternoon train, it reaches Goa at about 2300 hours.
You can look up train details on the websites,
http://www.konkanrailway.com or
http://www.indianrail.gov.in
Have a great trip.
Smartpati
but we wish to see a little of India and have the time to take it a little slower. I've done a general search on the net for transport and only found a couple of sites, and I don't think I'm finding the full choice out there. Does anyone have any info, names etc that I can research to get an idea of what may be on offer? 
Otherwise it's a 12 hour wait til evening to catch the later train.
